We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on 'identification at infinity' which leads to non-standard convergence rate. Andrews and Schafgans (1998) derived asymptotic results for a smoothed version of the estimator. We examine the optimal bandwidth selection for the estimators and derive asymptotic MSE rates under a wide class of distributional assumptions. We also provide some comparisons of the estimators and practical guidelines.